When I was taking advanced vector calculus 2, we were working out points in Nth dimensional space. In one lecture the professor Alek was trying to show us symbolically where a point in 12th dimensional space was. He had white board marker in between his fingers, and he was rotating both of his hands to show us where this point was. We were working with advanced antenna design, trying to optimize for noise, strength, stability, and some other properties. The thing was, he had the point in the mirrored position, and I symbolically got it right away, that he had the right alignment, but it was flipped, it's really difficult to accurately describe, but think of a classic X, Y, Z plot. Basically, he had the point at X = 1, when it was X = -1, much more complicated, but that's the idea. The entire lecture was him and me arguing about this point, and the reason it mattered was due to stability, noise, and strength of the antenna. To be fair, the point being mirrored didn't cause everything to fail, or have terrible performance, it was just less than ideal. After nearly an hour of this discussion, he put it to me to design my antenna using the mirrored point, and sure enough, my antenna was just a slight bit more stable, noise resistant, and its strength was better.
What is the point of that story? We're not teaching kids, in my experience, how to think about the problem being solved. They're running through the motions, they get an answer, they don't care, and they move on. When it's long division or simple multiplication, okay, fine, but, when you move on, and you're starting trig, or applied math, now it matters. Is your fraction correct? How do you know? How do you check? Regardless if you're doing the box thing, or a ribbon (I don't know what that is), or something else that's new, it all has to build on the fundamentals.
Teach the box method, that's fine, but also teach the classic method, and show kids how to contrast them, and if they disagree, how to try and figure out why? What really triggers me about this, if a kid completely misunderstood the plot to a story, it wouldn't be taken lightly, or shrugged off. If they don't understand why you should respect a persons pronouns, again, it would not be shrugged off. When it comes to math, it's shrugged off, and I've worked with Jr Engineers who couldn't tell you whether X should be between 2 and 10 or in a literal case, 2 trillion and 5 trillion. In that specific case, they used one method to compute X, instead of two, three or four methods. They didn't grasp what X was, and why it mattered, the value was 7.something, and that lack of awareness, will never fail to bother me.
As for the drawing stuff, have them do it once, twice, or several times, but if they can show they understand, then cut it out. The answer is what matters, but in between the question and the answer, let them solve it their own way, providing they get the right answer, and can defend that answer.